P5 Percentage: The Complete Guide

“Per cent” literally means “out of 100.” Once you understand that one idea, percentage questions become fraction questions you already know how to solve. This guide walks you through every P5 percentage skill — from basic conversions all the way to GST and discounts.

What Does “Per Cent” Mean?

The word percent comes from the Latin per centum — per (for every) + centum (hundred).

$1\% = \frac{1}{100}$

That’s the entire secret. Whenever you see the % sign, you can replace it with $\div 100$ or $\frac{}{100}$ .

Symbol	Meaning	Fraction
1%	1 out of 100	$\frac{1}{100}$
25%	25 out of 100	$\frac{25}{100}$
100%	All of it	$\frac{100}{100} = 1$

💡 The 100-Grid Trick

Imagine a 10 × 10 grid with 100 tiny squares. If 37 squares are shaded, that’s 37%. If all 100 are shaded, that’s 100%. Simple!

Part 1: Converting Fractions to Percentages

There are two methods. Pick whichever feels easier for the question.

Method 1: Make the Denominator 100

If you can turn the denominator into 100, the numerator becomes the percentage.

Example 1: Denominator of 20

Convert $\frac{17}{20}$ to a percentage.

Step 1: What do I multiply 20 by to get 100? → $20 \times 5 = 100$

Step 2: Multiply top and bottom by 5:

$\frac{17 \times 5}{20 \times 5} = \frac{85}{100}$

Step 3: Read off the numerator → 85%

Example 2: Denominator of 25

Express $\frac{9}{25}$ as a percentage.

$25 \times 4 = 100$

$\frac{9 \times 4}{25 \times 4} = \frac{36}{100} = 36\%$

Answer: 36%

Method 2: Multiply by 100%

This works for any fraction — even when the denominator doesn’t divide neatly into 100.

$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\%$

Example 3: Denominator of 5

Convert $\frac{3}{5}$ to a percentage.

$\frac{3}{5} \times 100\% = \frac{300}{5}\% = 60\%$

Answer: 60%

Common Fractions You Should Memorise

Fraction	Percentage	Fraction	Percentage
$\frac{1}{2}$	50%	$\frac{1}{5}$	20%
$\frac{1}{4}$	25%	$\frac{2}{5}$	40%
$\frac{3}{4}$	75%	$\frac{3}{5}$	60%
$\frac{1}{10}$	10%	$\frac{4}{5}$	80%

💡 Speed Hack

Knowing these by heart saves time in exams. $\frac{3}{4}$ ? You should instantly think “75%” without any calculation.

Part 2: Converting Decimals to Percentages (and Back)

Decimal → Percentage: Multiply by 100

This is just the decimal slide trick from your decimals chapter — move the decimal point 2 places to the right.

Decimal	× 100	Percentage
0.4	$0.4 \times 100$	40%
0.85	$0.85 \times 100$	85%
0.06	$0.06 \times 100$	6%
1.2	$1.2 \times 100$	120%

Percentage → Decimal: Divide by 100

Move the decimal point 2 places to the left.

Percentage	÷ 100	Decimal
23%	$23 \div 100$	0.23
7%	$7 \div 100$	0.07
150%	$150 \div 100$	1.5

Percentage → Fraction: Write Over 100, Then Simplify

Example: 75% to Fraction

Convert 75% to a fraction in simplest form.

Step 1: Write over 100 → $\frac{75}{100}$

Step 2: Simplify (HCF of 75 and 100 is 25):

$\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$

Answer: $\frac{3}{4}$

⚠️ Don't Forget to Simplify!

The question usually says “in simplest form.” $\frac{75}{100}$ alone won’t get full marks — you need $\frac{3}{4}$ .

Part 3: Finding Percentage of a Quantity

This is one of the most tested skills. The formula is:

$X\% \text{ of } Y = \frac{X}{100} \times Y$

Example 1: Simple Percentage

A shop has 500 items. 20% of them are on sale. How many items are on sale?

$\frac{20}{100} \times 500 = \frac{1}{5} \times 500 = 100$

Answer: 100 items

Example 2: Finding the Remainder

There are 800 people at a parade. 60% are adults. How many children are there?

Method 1: Find adults, then subtract.

Adults = $\frac{60}{100} \times 800 = 480$

Children = $800 - 480 = 320$

Method 2 (faster): Find children’s percentage first.

Children = $100\% - 60\% = 40\%$

$\frac{40}{100} \times 800 = 320$

Answer: 320 children

Example 3: With Mixed Units

A bottle holds 2 litres of water. 25% is poured out. How many ml is poured out?

Step 1: Convert to ml first → 2 ℓ = 2000 ml

Step 2: $\frac{25}{100} \times 2000 = \frac{1}{4} \times 2000 = 500$

Answer: 500 ml

Part 4: Finding What Percentage a Part Is

The reverse question: “What percentage is 45 out of 50?”

$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\%$

Example 1: Test Score

45 out of 50 students attended the camp. What percentage attended?

$\frac{45}{50} \times 100\% = 45 \times 2\% = 90\%$

Answer: 90%

Example 2: Multi-Step

A library has 200 books. 80 are fiction, 60 are non-fiction, and the rest are comics. What percentage are comics?

Step 1: Find comics → $200 - 80 - 60 = 60$

Step 2: Calculate percentage:

$\frac{60}{200} \times 100\% = 30\%$

Answer: 30%

Example 3: Different Units

Express 400 g as a percentage of 2 kg.

Step 1: Make units the same → 2 kg = 2000 g

Step 2: $\frac{400}{2000} \times 100\% = \frac{1}{5} \times 100\% = 20\%$

Answer: 20%

❌ Classic Trap: Different Units!

You CANNOT write $\frac{400}{2}$ when the part is in grams and the whole is in kilograms. Always convert to the same unit first.

Part 5: Pie Charts and Percentages

A pie chart shows how a whole is split into parts. The whole pie = 100%.

Reading Pie Charts

Example: Transport Survey

A pie chart shows how 100 students travel to school. Bus: 40, MRT: 25, Car: 20, Walk: ?. How many students walk?

Total = 100

Known = $40 + 25 + 20 = 85$

Walk = $100 - 85 = 15$

Answer: 15 students (which is also 15%)

Fractions in Pie Charts

Sometimes pie charts use fractions instead of numbers. Remember: the whole pie = 1 (or 100%).

Example: CCA Participation

A pie chart shows CCA choices. Sports is $\frac{1}{2}$ , Arts is $\frac{3}{10}$ , and Clubs is the rest. What percentage chose Clubs?

Step 1: Convert to common denominator (10):

$\frac{1}{2} = \frac{5}{10}$

Step 2: Find Clubs:

$1 - \frac{5}{10} - \frac{3}{10} = \frac{2}{10} = \frac{1}{5}$

Step 3: Convert to percentage:

$\frac{1}{5} \times 100\% = 20\%$

Answer: 20%

Finding Amounts from Pie Charts

Example: Allowance Pie Chart

John’s monthly allowance is $200. Food: 50%, Savings: 30%, Transport: 20%. How much more does he save than spend on transport?

Method 1: Find amounts, then subtract.

Savings = $30\%$ of 200 = $60

Transport = $20\%$ of 200 = $40

Difference = $60 − $40 = $20

Method 2 (faster): Find percentage difference first.

$30\% - 20\% = 10\%$

$10\%$ of 200 = $20

Answer: $20

Part 6: Real-World Percentage — GST, Discounts & Interest

This is where percentage becomes truly useful. These topics are uniquely important for students in Singapore!

GST (Goods and Services Tax) — 9%

In Singapore, most purchases include a 9% GST on top of the listed price.

Example 1: Calculate GST

A laptop costs $1000 before GST. What is the total price including 9% GST?

Step 1: Calculate GST amount:

$\frac{9}{100} \times 1000 = 90$

GST = $90

Step 2: Add to original price:

$1000 + $90 = $1090

Example 2: GST on a Meal

A meal costs $50 before GST. What is the final bill?

GST = $\frac{9}{100} \times 50$ = $4.50

Total = $50 + $4.50 = $54.50

💡 Quick GST Trick

To find 9% quickly: find 10% (move the decimal one place left), then subtract 1%. For $50: 10% = $5, 1% = $0.50, so 9% = $5 - $0.50 = $4.50.

Discounts

A discount reduces the price. You calculate the discount amount, then subtract it.

Example: Great Singapore Sale

A bag has a usual price of $80. It has a 10% member discount. What is the price after discount?

Step 1: Discount = $\frac{10}{100} \times 80$ = $8

Step 2: Discounted price = $80 − $8 = $72

Simple Interest

When you save money in a bank, the bank pays you interest — extra money for keeping your savings with them.

Example: Bank Savings

Siti deposits $5000 in a bank at 3% interest per year. What is her total amount after 1 year?

Step 1: Interest = $\frac{3}{100} \times 5000$ = $150

Step 2: Total = $5000 + $150 = $5150

The Big Rule: Add or Subtract?

Situation	What Happens	Operation
GST	Price goes UP	Original + GST
Discount	Price goes DOWN	Original − Discount
Interest	Savings go UP	Principal + Interest

Challenge: Discount + GST Combined

A watch costs $200. There is a 10% discount. After the discount, 9% GST is applied on the discounted price. What is the final price?

Step 1: Discount = $10\%$ of 200 = $20

Discounted price = $200 − $20 = $180

Step 2: GST = $9\%$ of 180 = $16.20

Step 3: Final price = $180 + $16.20 = $196.20

⚠️ Order Matters!

Always calculate the discount first, then apply GST on the discounted price — not the original price. This is how it works in real life and in exam questions.

Try the Percentage Calculator

Use this interactive calculator to check your work or explore percentage calculations:

Percentage Calculator

What do you want to calculate?

Original Value

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Common Mistakes to Avoid

❌ Mistake 1: Forgetting to Convert Units

“Express 500 ml as a percentage of 2 ℓ.” You must convert 2 ℓ to 2000 ml first. Writing $\frac{500}{2}$ gives you 250%, which is nonsense!

❌ Mistake 2: Part vs Whole Confusion

“40 out of 200 marbles are red. What percentage?” The part is 40 (red marbles) and the whole is 200 (all marbles). It’s $\frac{40}{200}$ , not $\frac{200}{40}$ .

❌ Mistake 3: Not Simplifying the Fraction

When the question says “in simplest form,” $\frac{75}{100}$ loses marks. Always simplify to $\frac{3}{4}$ .

⚠️ Mistake 4: Adding GST to the Original After Discount

If there’s a 10% discount on $200 and then 9% GST, the GST is on $180 (the discounted price), NOT on $200. Getting this wrong gives you the wrong final answer.

Quick Reference Cheat Sheet

Task	Formula	Example
Fraction → %	$\frac{a}{b} \times 100\%$	$\frac{3}{5} \times 100\% = 60\%$
Decimal → %	$d \times 100$	$0.85 \times 100 = 85\%$
% → Decimal	$p \div 100$	$23 \div 100 = 0.23$
% → Fraction	$\frac{p}{100}$ , simplify	$\frac{75}{100} = \frac{3}{4}$
X% of Y	$\frac{X}{100} \times Y$	$20\%$ of $500 = 100$
Part is what % of Whole?	$\frac{\text{Part}}{\text{Whole}} \times 100\%$	$\frac{45}{50} \times 100\% = 90\%$
GST (9%)	Price + 9% of Price	$100 + $9 = $109
Discount	Price − X% of Price	$80 − $8 = $72

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P5 Percentage: The Complete Guide (Fractions, Decimals & GST)